Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+9y &= -2 \\ -x+3y &= -6\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = x-6$ Divide both sides by $3$ to isolate $y$ $y = {\dfrac{1}{3}x - 2}$ Substitute this expression for $y$ in the first equation. $-7x+9({\dfrac{1}{3}x - 2}) = -2$ $-7x + 3x - 18 = -2$ Simplify by combining terms, then solve for $x$ $-4x - 18 = -2$ $-4x = 16$ $x = -4$ Substitute $-4$ for $x$ back into the top equation. $-7( -4)+9y = -2$ $28+9y = -2$ $9y = -30$ $y = -\dfrac{10}{3}$ The solution is $\enspace x = -4, \enspace y = -\dfrac{10}{3}$.